An alternative point of view for you to consider integrating into your framework — falsifiability.
Karl Popper wrote in depth on this topic, and when truly understood it enhances the understanding of “proof”. Specifically, the idea is we can only truly prove what is *not*, and by doing enough of that, limit the “truth” to a smaller and smaller area of ignorance. Imagine a room where we’re looking for some lost item, and through our facts and evidence, we’re able to exclude large areas, and know that while we may not directly observe the lost item, we know it’s location is bounded by areas we’ve excluded.
To play the game in the most efficient way, we use what is called a necessary and sufficient falsifiable hypothesis, to wit:
- a list of observations that would falsify our hypothesis;
- an argument that shows that the lack of those falsification criteria would exclude other hypotheses, including the null.
The tricky part really is understanding that we never increase knowledge, we only really reduce ignorance :). If we can adhere to these kinds of rules, we can have an objective standard, although the sad truth is not everything is amenable to this kind of objective approach. Even the most pure mathematical systems cannot avoid internal contradiction, which suggests that while we may reduce our ignorance a great deal, there are certain mysteries that are truly beyond understanding.